Positive Solutions to a Second Order Multi-point Boundary-value Problem
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We prove the existence of positive solutions to the boundary-value problem
u" + λα(t) ƒ (u,u') = 0
u(0) = 0, u(1) = ∑m-2i=1 αiu(↋i),
where α is a continuous function that may change sign on [0,1], ƒ is a continuous function with ƒ (0,0) > 0, and λ is a samll positive constant. For finding solutions we use the Leray-Schauder fixed point theorem.
CitationCao, D., & Ma, R. (2000). Positive solutions to a second order multi-point boundary-value problem. Electronic Journal of Differential Equations, 2000(65), pp. 1-8.
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